Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-3x-6y &= -9 \\ -4x+4y &= 1\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $-4x = -4y+1$ Divide both sides by $-4$ to isolate $x$ $x = {y - \dfrac{1}{4}}$ Substitute this expression for $x$ in the first equation. $-3({y - \dfrac{1}{4}}) - 6y = -9$ $-3y + \dfrac{3}{4} - 6y = -9$ Simplify by combining terms, then solve for $y$ $-9y + \dfrac{3}{4} = -9$ $-9y = -\dfrac{39}{4}$ $y = \dfrac{13}{12}$ Substitute $\dfrac{13}{12}$ for $y$ in the top equation. $-3x-6( \dfrac{13}{12}) = -9$ $-3x-\dfrac{13}{2} = -9$ $-3x = -\dfrac{5}{2}$ $x = \dfrac{5}{6}$ The solution is $\enspace x = \dfrac{5}{6}, \enspace y = \dfrac{13}{12}$.